Final answer:
To solve the problem, algebraic equations are formulated using the given ratios of the women's ages. The variable x is determined to be 10, which leads to the present ages of the two women being 30 and 40 years, respectively.
Step-by-step explanation:
To find the present ages of the two women given that the ratio of their ages is 3/4 and was 5/7 five years ago, we'll use the concept of ratios and algebraic equations. Let the present ages of the two women be 3x and 4x, respectively. Five years ago, their ages would have been (3x - 5) and (4x - 5).
Now, we set up the equation based on the ratio given for five years ago: (3x - 5)/(4x - 5) = 5/7. Multiplying both sides by (4x - 5) and then by 7 to clear the fractions gives us 21x - 35 = 20x - 25. Simplifying this gives us x = 10.
Substituting x back into our present ages expressions gives us the current ages as 3x = 30 years and 4x = 40 years for the two women.